One can model a LQG black hole at the kinematical level as a space
region bounded by a closed surface -the horizon- whose geometry an
external observer can acquire information about only through
measurements on the surface. The black hole state is then given by
completely coarse-graining the geometry of the bounded region, which
defines a density matrix on the space of intertwiners i.e. the quantum
state of the boundary horizon. I'll explain how to derive the black hole
entropy law in that context and how to explain the logarithmic
correction in terms of entanglement/correlation between parts of the
horizon. This will lead to introduce a concept of surface
renormalisationin LQG.